基于改进的对数周期幂律模型研究中国股市崩盘预警

吴俊传; 唐振鹏; 杜晓旭; 陈凯杰

doi:10.7498/aps.71.20201940

摘要

基于金融物理学中著名的对数周期幂律模型(log-periodic power law model, LPPL)来预警2015年6月份中国上证综合指数、创业板指数的崩盘. 鉴于已有采用LPPL模型预警市场崩盘的研究均只考虑市场历史交易数据. 本文将投资者情绪因素纳入到LPPL模型建模过程, 以改进LPPL模型的预警效果. 采用文本挖掘技术结合语义分析方法对抓取的财经媒体的股评报道进行词频统计, 以构建媒体情绪指数. 进一步修改LPPL模型中的崩溃概率函数表达式, 将其表示为关于历史交易数据及媒体情绪的函数, 构建LPPL-MS组合模型预警股市崩盘. 实证结果表明, 本文所构建的LPPL-MS组合模型相比LPPL模型具有更高的预警精度, 其预测的大盘见顶的临界时点与上证指数、创业板指数真实的见顶时点更为接近, 并且其拟合结果通过了相关检验.

关键词:

Abstract

This paper is based on the famous log-periodic power law model (LPPL) in financial physics to warn of the collapse of China's Shanghai Composite Index and GEM Index in June 2015. In view of the existing research using the LPPL model to warn of market crash, only the historical trading data of the market are considered. For the first time, investor sentiment factors are incorporated into the modeling process of LPPL model to improve the early warning effect of LPPL model. Using the text mining technology combined with semantic analysis methods to grasp the financial media's stock evaluation report for word frequency statistics, in order to build the medium sentiment index. The further modified expression of the crash probability function in the LPPL model is represented as a function of historical trading data and medium sentiment, and thus constructing an LPPL-MS combination model to warn of stock market crash. The empirical results show that the LPPL-MS combination model constructed in this paper has higher warning accuracy than the LPL model, and its prediction crash time is closer to the actual crash time of the Shanghai Index and GEM Index, and its fitting results have passed the relevant test.

Keywords:

作者及机构信息

福州大学经济与管理学院, 福州　350108

通信作者: 唐振鹏, zhenpt@126.com

基金项目: 国家自然科学基金(批准号: 71573042, 71973028)资助的课题

Authors and contacts

School of Economics and Management, Fuzhou University, Fuzhou 350108, China

Corresponding author: Tang Zhen-Peng, zhenpt@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 71573042, 71973028)

文章全文 : translate this paragraph

参考文献

[1]	Sornette D, Johansen A, Bouchaud J P 1995 J. Phys. I. 6 167 Google Scholar
[2]	Johansen A, Sornette D 1999 Risk. 12 91
[3]	Jensen M C 1967 Financ. Anal. J. 23 77
[4]	Fama U 1965 J. Bus. 38 34 Google Scholar
[5]	蒋志强, 田婧雯, 周炜星 2019 管理科学学报 22 92 Google Scholar Jiang Z Q, Tian J W, Zhou W X 2019 J. Manag. Sci. China 22 92 Google Scholar
[6]	徐翔, 朱承, 朱先强 2021 物理学报 70 088901 Google Scholar Xu X, Zhu C, Zhu X Q 2021 Acta Phys. 70 088901 Google Scholar
[7]	Gurkaynak R S 2008 J. Econ. Sury. 22 166 Google Scholar
[8]	Bak P, Tang C, Wiesenfeld K 1987 Phys. Rev. Lett. 59 381 Google Scholar
[9]	潘娜, 王子剑, 周勇 2018 中国管理科学 26 25 Google Scholar Pan N, Wang Z J, Zhou Y 2018 Chin. J. Manag. Sci. 26 25 Google Scholar
[10]	周炜星 2007 金融物理学导论 (上海: 上海财经大学出版社) 第17—33页 Zhou W X 2007 Introduction of Econophysics (Shang-hai: Shanghai University of Finance and Economics Press) pp17–33 (in Chinese)
[11]	Sornette D, Johansen A 1997 Physica A 245 411 Google Scholar
[12]	Sornette D, Johansen A 1998 Physica A 261 581 Google Scholar
[13]	Sornette D, Zhou W X 2006 Int. J. Forecast 22 153 Google Scholar
[14]	Sornette D, Woodard R, Zhou W X 2009 Physica A 388 1571 Google Scholar
[15]	Kyriazis N, Papadamou S, Corbet S 2020 Res. Int. Bus. Financ. 54 101254 Google Scholar
[16]	Omer O 2020 Eur. Phys. J. Spec. Top. 229 1715 Google Scholar
[17]	Sirca S J, Omladic M 2020 ARS Math. Contemp. 13 63
[18]	Filimonov V, Sornette D 2013 Physica A 392 3698 Google Scholar
[19]	Jiang Z, Zhou W X, Sornette D, et al. 2010 J. Econ. Behav. Organ. 74 149 Google Scholar
[20]	Yan W, Rebib R, Woodard R, Sornette D 2012 IJPAM. 1 59 Google Scholar
[21]	李东 2012 淮海工学院学报(自然科学版) 21 4 Li D 2012 J. Huaihai Insti of Tech. (Natural Science Edition) 21 4
[22]	周伟, 何建敏 2011 金融研究 375 65 Zhou W, He J M 2011 J. Financ. Res. 375 65
[23]	李斯嘉, 李冬昕, 王粟旸 2017 上海经济研究 7 42 Li S J, Li D X, Wang L Y 2017 Shanghai J. Econ. 7 42
[24]	李伦一, 张翔 2019 金融研究 474 169 Li L Y, Zhang X 2019 J. Financ. Res. 474 169
[25]	陈卫华, 蔡文靖 2018 统计与决策 497 143 Google Scholar Chen W H, Cai W J 2018 Statistics and Decision 497 143 Google Scholar
[26]	赵磊, 刘庆 2020 统计与决策 558 128 Google Scholar Zhao L, Liu Q 2020 Statistics and Decision 558 128 Google Scholar
[27]	Kahneman D 2003 Am. Econ. Rev. 93 1449 Google Scholar
[28]	Baker M, Wurgler J 2006 J. Financ. 61 1645 Google Scholar
[29]	Baker M, Wurgler J 2007 J. Econ. Perspect 21 129 Google Scholar
[30]	García D 2013 J. Financ. 68 1267 Google Scholar
[31]	Fang L, Peress J 2009 J. Financ. 64 2023 Google Scholar
[32]	Barber B M, Odean T 2008 Rev. Financ. Stud. 21 785 Google Scholar
[33]	Solomon D H 2012 J. Financ. 67 599 Google Scholar
[34]	Nardo M, Petracco-Giudici M, Naltsidis M 2016 J. Econ. Surv. 30 356 Google Scholar
[35]	Fisher K L, Statman M 2000 Financ. Anal. J. 56 16 Google Scholar
[36]	武佳薇, 汪昌云, 陈紫琳, Jie Michael Guo 2020 金融研究 476 147 Wu J W, Wang C Y, Chen Z L, Jie M G 2020 J. Financ. Res. 476 147
[37]	李合龙, 冯春娥 2014 系统工程理论与实践 34 2495 Google Scholar Li H L, Feng C E 2014 System Eng. Theor. Prac. 34 2495 Google Scholar
[38]	游家兴, 吴静 2012 经济研究 534 141 You J X, Wu J 2012 Econ. Res. J 534 141
[39]	Wu D D, Zheng L, Olson D L 2014 IEEE T. SYST Man CY-S. 44 1077 Google Scholar
[40]	戴德宝, 兰玉森, 范体军, 赵敏 2019 中国软科学 340 166 Google Scholar Dai D B, Lan Y S, Fan T J, Zhao M 2019 China Soft Sci. 340 166 Google Scholar
[41]	Martin G 1971 In Computers, Communication, and the Public Interest (Baltimore, MD: The Johns Hopkins Press) p37
[42]	Da Z, Engelberg J, Gao P 2011 J. Financ. 66 1461 Google Scholar
[43]	Huang X, Nekrasov A, Teoh S H 2018 Account. Rev. 93 231 Google Scholar
[44]	Sentiment Analysis, Bian S B, Jia D K, Li F http://dx.doi.org/10.2139/ssrn.3446388 [2020-11-10]
[45]	王晓丹, 尚维, 汪寿阳 2019 系统工程理论与实践 39 3038 Google Scholar Wang X D, Shang W, Wang S Y 2019 System Eng. Theor. Prac. 39 3038 Google Scholar
[46]	Johansen A, Ledoit O, Sornette D. 2000 Int J Theor Appl Finan. 3 219 Google Scholar
[47]	Yan W F, Woodard R, Sornette D 2014 Quant. Financ. 14 1273 Google Scholar
[48]	Lin L, Sornette D 2013 Eur. J. Financ. 19 344 Google Scholar

施引文献

图 1 上证指数2015年泡沫期间LPPL拟合图

Fig. 1. LPPL fitting diagram of the Shanghai stock exchange (SSE) index during the 2015 bubble.

下载: 全尺寸图片幻灯片

图 2 部分财经媒体评论稿标题信息样本

Fig. 2. Some financial media commentary title information samples.

下载: 全尺寸图片幻灯片

图 3 上证指数、创业板指数泡沫前后走势

Fig. 3. Trend of SSE index and growth enterprise market (GEM) index before and after bubble.

下载: 全尺寸图片幻灯片

图 4 上证指数、创业板指数不同模型预测表现比较分析

Fig. 4. Comparative analysis of forecasting performance of different models of Shanghai Stock Exchange Index and Growth Enterprise Market Index.

下载: 全尺寸图片幻灯片

表 1 CFSD词典部分积极、消极词汇

Table 1. Some positive and negative words in CFSD dictionary.

序号	积极词汇	消极词汇
1	突破	拖累
2	增长	不涨反跌
3	高涨	分化
4	火爆	沉重打击
5	赚钱	恐慌
6	上升	下降
7	一枝独秀	狂跌
8	蒸蒸日上	跌停板
9	活跃	退市
10	提速	暴涨暴跌

下载: 导出CSV

表 2 (MS)序列描述性统计分析

Table 2. Descriptive statistical analysis of media sentiment(MS) sequence.

最大值	最小值	均值	标准差	偏度	峰度
1.794	–0.998	0.252	0.446	0.037	3.158

下载: 导出CSV

表 3 上证指数LPPL, LPPL-MS参数估计结果

Table 3. Parameter estimation results of SSE index LPPL and LPPL-MS.

	MSE	A	B	C	m	ω	ϕ	λ	$ {t_{\text{c}}} $
LPPL	0.997	10.131	–0.864	–0.017	0.188	12.098	1.748	—	369.022
	1.078	10.161	–0.828	–0.015	0.197	11.991	1.840	—	379.036
	1.112	9.949	–0.805	0.014	0.188	10.368	2.029	—	361.668
LPPL-MS	0.948	9.639	–0.562	–0.014	0.226	12.398	6.686	0.008	362.729
	0.991	9.597	–0.509	–0.013	0.240	12.911	3.717	0.007	365.669
	1.038	9.552	–0.508	–0.012	0.237	12.953	3.671	0.010	360.949

下载: 导出CSV

表 4 创业板指数LPPL、LPPL-MS参数估计结果

Table 4. Estimation results of LPPL and LPPL-MS parameters of gem index.

	MSE	A	B	C	m	ω	ϕ	λ	$ {t_{\text{c}}} $
LPPL	2.429	8.444	–0.334	0.006	0.239	13.988	2.241	—	335.923
	2.443	8.654	–0.436	–0.015	0.217	13.009	3.989	—	341.826
	2.477	8.517	–0.355	–0.011	0.236	13.039	3.998	—	340.435
LPPL-MS	2.703	8.617	–0.395	0.011	0.229	15.242	0.288	0.015	344.122
	2.819	9.218	–0.766	0.016	0.174	16.445	5.320	0.010	352.216
	2.904	8.922	–0.559	0.010	0.200	21.717	0.256	0.010	353.759

下载: 导出CSV

表 5 上证指数、创业板指数预警误差比较分析

Table 5. Comparative analysis of early warning errors between SSE index and GEM index.

		最低绝对误差	最高绝对误差	平均绝对误差
LPPL	上证指数	9	27	18
LPPL	创业板指	4	10	7
LPPL-MS	上证指数	8^*	13^*	11^*
LPPL-MS	创业板指	1^*	8^*	6^*
注: *表明预测的见顶时点最接近真实值.

下载: 导出CSV

表 6 上证指数、创业板指数不同拟合情形下残差平稳性检验

Table 6. Residual stationarity test of SSE index and GEM index under different fitting conditions.

		拟合情形1	拟合情形2	拟合情形3
LPPL	上证指数	0.014^**	0.021^**	0.013^**
LPPL	创业板指	0.0428^**	0.073^*	0.0959^*
LPPL-MS	上证指数	0.001^***	0.001^***	0.012^**
LPPL-MS	创业板指	0.019^**	0.041^**	0.074^*
注: 表明在10%水平下显著; 表明在5%水平下显著; **表明在1%水平下显著.

下载: 导出CSV

[1]	Sornette D, Johansen A, Bouchaud J P 1995 J. Phys. I. 6 167 Google Scholar
[2]	Johansen A, Sornette D 1999 Risk. 12 91
[3]	Jensen M C 1967 Financ. Anal. J. 23 77
[4]	Fama U 1965 J. Bus. 38 34 Google Scholar
[5]	蒋志强, 田婧雯, 周炜星 2019 管理科学学报 22 92 Google Scholar Jiang Z Q, Tian J W, Zhou W X 2019 J. Manag. Sci. China 22 92 Google Scholar
[6]	徐翔, 朱承, 朱先强 2021 物理学报 70 088901 Google Scholar Xu X, Zhu C, Zhu X Q 2021 Acta Phys. 70 088901 Google Scholar
[7]	Gurkaynak R S 2008 J. Econ. Sury. 22 166 Google Scholar
[8]	Bak P, Tang C, Wiesenfeld K 1987 Phys. Rev. Lett. 59 381 Google Scholar
[9]	潘娜, 王子剑, 周勇 2018 中国管理科学 26 25 Google Scholar Pan N, Wang Z J, Zhou Y 2018 Chin. J. Manag. Sci. 26 25 Google Scholar
[10]	周炜星 2007 金融物理学导论 (上海: 上海财经大学出版社) 第17—33页 Zhou W X 2007 Introduction of Econophysics (Shang-hai: Shanghai University of Finance and Economics Press) pp17–33 (in Chinese)
[11]	Sornette D, Johansen A 1997 Physica A 245 411 Google Scholar
[12]	Sornette D, Johansen A 1998 Physica A 261 581 Google Scholar
[13]	Sornette D, Zhou W X 2006 Int. J. Forecast 22 153 Google Scholar
[14]	Sornette D, Woodard R, Zhou W X 2009 Physica A 388 1571 Google Scholar
[15]	Kyriazis N, Papadamou S, Corbet S 2020 Res. Int. Bus. Financ. 54 101254 Google Scholar
[16]	Omer O 2020 Eur. Phys. J. Spec. Top. 229 1715 Google Scholar
[17]	Sirca S J, Omladic M 2020 ARS Math. Contemp. 13 63
[18]	Filimonov V, Sornette D 2013 Physica A 392 3698 Google Scholar
[19]	Jiang Z, Zhou W X, Sornette D, et al. 2010 J. Econ. Behav. Organ. 74 149 Google Scholar
[20]	Yan W, Rebib R, Woodard R, Sornette D 2012 IJPAM. 1 59 Google Scholar
[21]	李东 2012 淮海工学院学报(自然科学版) 21 4 Li D 2012 J. Huaihai Insti of Tech. (Natural Science Edition) 21 4
[22]	周伟, 何建敏 2011 金融研究 375 65 Zhou W, He J M 2011 J. Financ. Res. 375 65
[23]	李斯嘉, 李冬昕, 王粟旸 2017 上海经济研究 7 42 Li S J, Li D X, Wang L Y 2017 Shanghai J. Econ. 7 42
[24]	李伦一, 张翔 2019 金融研究 474 169 Li L Y, Zhang X 2019 J. Financ. Res. 474 169
[25]	陈卫华, 蔡文靖 2018 统计与决策 497 143 Google Scholar Chen W H, Cai W J 2018 Statistics and Decision 497 143 Google Scholar
[26]	赵磊, 刘庆 2020 统计与决策 558 128 Google Scholar Zhao L, Liu Q 2020 Statistics and Decision 558 128 Google Scholar
[27]	Kahneman D 2003 Am. Econ. Rev. 93 1449 Google Scholar
[28]	Baker M, Wurgler J 2006 J. Financ. 61 1645 Google Scholar
[29]	Baker M, Wurgler J 2007 J. Econ. Perspect 21 129 Google Scholar
[30]	García D 2013 J. Financ. 68 1267 Google Scholar
[31]	Fang L, Peress J 2009 J. Financ. 64 2023 Google Scholar
[32]	Barber B M, Odean T 2008 Rev. Financ. Stud. 21 785 Google Scholar
[33]	Solomon D H 2012 J. Financ. 67 599 Google Scholar
[34]	Nardo M, Petracco-Giudici M, Naltsidis M 2016 J. Econ. Surv. 30 356 Google Scholar
[35]	Fisher K L, Statman M 2000 Financ. Anal. J. 56 16 Google Scholar
[36]	武佳薇, 汪昌云, 陈紫琳, Jie Michael Guo 2020 金融研究 476 147 Wu J W, Wang C Y, Chen Z L, Jie M G 2020 J. Financ. Res. 476 147
[37]	李合龙, 冯春娥 2014 系统工程理论与实践 34 2495 Google Scholar Li H L, Feng C E 2014 System Eng. Theor. Prac. 34 2495 Google Scholar
[38]	游家兴, 吴静 2012 经济研究 534 141 You J X, Wu J 2012 Econ. Res. J 534 141
[39]	Wu D D, Zheng L, Olson D L 2014 IEEE T. SYST Man CY-S. 44 1077 Google Scholar
[40]	戴德宝, 兰玉森, 范体军, 赵敏 2019 中国软科学 340 166 Google Scholar Dai D B, Lan Y S, Fan T J, Zhao M 2019 China Soft Sci. 340 166 Google Scholar
[41]	Martin G 1971 In Computers, Communication, and the Public Interest (Baltimore, MD: The Johns Hopkins Press) p37
[42]	Da Z, Engelberg J, Gao P 2011 J. Financ. 66 1461 Google Scholar
[43]	Huang X, Nekrasov A, Teoh S H 2018 Account. Rev. 93 231 Google Scholar
[44]	Sentiment Analysis, Bian S B, Jia D K, Li F http://dx.doi.org/10.2139/ssrn.3446388 [2020-11-10]
[45]	王晓丹, 尚维, 汪寿阳 2019 系统工程理论与实践 39 3038 Google Scholar Wang X D, Shang W, Wang S Y 2019 System Eng. Theor. Prac. 39 3038 Google Scholar
[46]	Johansen A, Ledoit O, Sornette D. 2000 Int J Theor Appl Finan. 3 219 Google Scholar
[47]	Yan W F, Woodard R, Sornette D 2014 Quant. Financ. 14 1273 Google Scholar
[48]	Lin L, Sornette D 2013 Eur. J. Financ. 19 344 Google Scholar

[1]	李松蔚, 谢勇. 基于功率谱的神经元放电早期预警信号. 物理学报, 2025, 74(1): 010501. doi: 10.7498/aps.74.20241471
[2]	李斌, 张国峰, 景明勇, 陈瑞云, 秦成兵, 高岩, 肖连团, 贾锁堂. 利用单分子光学探针测量幂律分布的聚合物动力学. 物理学报, 2016, 65(21): 218201. doi: 10.7498/aps.65.218201
[3]	陈平, 韩焱, 潘晋孝. 基于对数解调的递变能量CT成像方法. 物理学报, 2015, 64(13): 138701. doi: 10.7498/aps.64.138701
[4]	杨建强, 马洪, 钟苏川. 分数阶对数耦合系统在非周期外力作用下的定向输运现象. 物理学报, 2015, 64(17): 170501. doi: 10.7498/aps.64.170501
[5]	郭进利. 非均齐超网络中标度律的涌现富者愈富导致幂律分布吗?. 物理学报, 2014, 63(20): 208901. doi: 10.7498/aps.63.208901
[6]	颜鹏程, 侯威, 胡经国. 基于Logistic模型的均值突变时间序列临界预警研究. 物理学报, 2012, 61(18): 189202. doi: 10.7498/aps.61.189202
[7]	尉伟峰. 选择理论生成幂律的扩展性研究. 物理学报, 2009, 58(10): 6696-6702. doi: 10.7498/aps.58.6696
[8]	尉伟峰. 基于选择模式的幂律生成机制. 物理学报, 2009, 58(4): 2127-2135. doi: 10.7498/aps.58.2127
[9]	支蓉, 龚志强. 利用幂律尾指数的中国降水突变检测与归因. 物理学报, 2008, 57(7): 4629-4633. doi: 10.7498/aps.57.4629
[10]	胡先权, 许杰, 马勇, 殷霖. 高次正幂与逆幂势函数的叠加的径向薛定谔方程的解析解. 物理学报, 2007, 56(9): 5060-5065. doi: 10.7498/aps.56.5060
[11]	支蓉, 廉毅, 封国林. 基于幂律尾指数研究不同尺度系统对降水的影响. 物理学报, 2007, 56(3): 1837-1842. doi: 10.7498/aps.56.1837
[12]	孙亮, 孙一峰, 马东军, 孙德军. 高瑞利数下水平自然热对流的幂律关系. 物理学报, 2007, 56(11): 6503-6507. doi: 10.7498/aps.56.6503
[13]	郭进利, 汪丽娜. 幂律指数在1与3之间的一类无标度网络. 物理学报, 2007, 56(10): 5635-5639. doi: 10.7498/aps.56.5635
[14]	唐驾时, 欧阳克俭. logistic模型的倍周期分岔控制. 物理学报, 2006, 55(9): 4437-4441. doi: 10.7498/aps.55.4437
[15]	支蓉, 龚志强, 王德英, 封国林. 基于幂律尾指数研究中国降水的时空演变特征. 物理学报, 2006, 55(11): 6185-6191. doi: 10.7498/aps.55.6185
[16]	郭进利. 供应链型网络中双幂律分布模型. 物理学报, 2006, 55(8): 3916-3921. doi: 10.7498/aps.55.3916
[17]	靳艳飞, 徐伟, 李伟, 徐猛. 具有周期信号调制噪声的线性模型的随机共振. 物理学报, 2005, 54(6): 2562-2567. doi: 10.7498/aps.54.2562
[18]	陈贺胜. 周期驱动的一维台球模型的量子扩散特性. 物理学报, 2000, 49(5): 844-848. doi: 10.7498/aps.49.844
[19]	刘文森, 马桂荣, 张九安, 梁九卿. 量子玻色流体中的压缩玻色子对数态. 物理学报, 1997, 46(9): 1699-1709. doi: 10.7498/aps.46.1699
[20]	李飞熊, 张一德, 安常福. 多晶铁磁体趋近饱和律的测试. 物理学报, 1978, 27(5): 604-608. doi: 10.7498/aps.27.604

计量

文章访问数: 6267
PDF下载量: 117
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板